{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# import modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 生成tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "a = torch.rand(2,3)         #[0,1]之间的均匀分布中抽取\n",
    "b = torch.randn(2,2)        #标准正态分布中抽取\n",
    "c = torch.arange(1,10,1)    #1开始每个加1，10结束\n",
    "d = torch.linspace(1,10,10) #1开始，10结束，总共10个数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variable(t, volatile=True)\n",
    "voliate:当一个tensor的requires_grad=True后，与a相连的张量的requires_grad都被设置为True （ps：c=a+b，c与a相连，b不与a相连）。\n",
    "\n",
    "而violate=True时，该Tensor的requires_grad=False,且相连的Tensor的requires_grad都被设置为False 的比requies_grad优先级别高"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/yinzp/.local/lib/python3.6/site-packages/ipykernel_launcher.py:2: UserWarning: volatile was removed and now has no effect. Use `with torch.no_grad():` instead.\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from torch.autograd import Variable\n",
    "a = Variable(torch.Tensor([1,2,3]), volatile=True)\n",
    "b = Variable(torch.Tensor([1,2,3]), requires_grad=False)\n",
    "z = a + b\n",
    "z.requires_grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 数据操作函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### torch.max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `torch.sort(dim=-1, descending=True)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([3., 1.])\n",
      "tensor([1, 0])\n",
      "tensor(1)\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "l = []\n",
    "l.append(torch.Tensor([1]))\n",
    "l.append(torch.Tensor([3]))\n",
    "l = torch.cat(l, 0)\n",
    "x = torch.tensor([3,7,2,6])\n",
    "z, y = l.sort(dim=0, descending=True)\n",
    "print(z)\n",
    "print(y)\n",
    "i = y[0]\n",
    "print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `torch.clamp()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([5, 7, 5, 6])\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "x = torch.tensor([3,7,2,6])\n",
    "y = x.clamp(min=5)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `torch.roll(inputs, shifts, dims=None)`\n",
    "\n",
    "inputs---tensors\n",
    "\n",
    "shifts--- the number of places by which the elements of the tensor are shifted\n",
    "\n",
    "dims--- Axis along which to roll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1, 2],\n",
      "        [3, 4],\n",
      "        [5, 6],\n",
      "        [7, 8]])\n",
      "tensor([[7, 8],\n",
      "        [1, 2],\n",
      "        [3, 4],\n",
      "        [5, 6]])\n"
     ]
    }
   ],
   "source": [
    "x = torch.tensor([1,2,3,4,5,6,7,8]).view(4,2)\n",
    "print(x)\n",
    "# shift the first axis(4) by one places\n",
    "x = torch.roll(x, 1, 0)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `tensor.mean(dim=[0,1,2])`,`tensor.var()`\n",
    "依次对tensor的0,1,2,维度求平均"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[[0., 1.],\n",
      "         [2., 3.]],\n",
      "\n",
      "        [[4., 5.],\n",
      "         [6., 7.]]])\n",
      "tensor([[2., 3.],\n",
      "        [4., 5.]])\n",
      "tensor([3., 4.])\n",
      "tensor(3.5000)\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "a = torch.arange(8, dtype=torch.float32).reshape(2,2,2)\n",
    "#a = torch.Tensor([[[1,2],[3,4]],[[5,6],[7,8]]])\n",
    "print(a)\n",
    "print(a.mean([0]))\n",
    "print(a.mean([0,1]))\n",
    "print(a.mean([0,1,2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `contiguous`\n",
    "Tensor多维数组底层实现是使用一块连续内存的1维数组（行优先顺序存储）。\n",
    "\n",
    "索引时，通过stride将二维索引转换为1维，根据1维数组头地址偏移取值。\n",
    "\n",
    "`transpose`,`permute`等函数只是改变了stride，使用新的stride查看数组。**指向的仍然是原来的一维数组**。transpose一次只能交换两个维度，permute能交换多个维度。\n",
    "\n",
    "`view()`仅在**底层数组上**使用指定的形状进行变形。\n",
    "\n",
    "`is_contiguous()`用来判断按新的stride取出来的数组，是否是按行连续存储的。\n",
    "\n",
    "`.contiguous()`开辟一块新的内存空间，将按新的stride取出来的数组，按行进行连续存储。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t: tensor([[ 0,  1,  2,  3],\n",
      "        [ 4,  5,  6,  7],\n",
      "        [ 8,  9, 10, 11]]) \n",
      " Is t contiguous? True\n"
     ]
    }
   ],
   "source": [
    "t = torch.arange(12).reshape(3,4)\n",
    "print('t:',t,'\\n',\"Is t contiguous?\",t.is_contiguous())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t: tensor([[ 0,  4,  8],\n",
      "        [ 1,  5,  9],\n",
      "        [ 2,  6, 10],\n",
      "        [ 3,  7, 11]]) \n",
      " Is t2 contiguous? False \n",
      " Is same data: True\n"
     ]
    }
   ],
   "source": [
    "t2 = t.transpose(0,1)\n",
    "print('t:',t2,'\\n',\n",
    "      \"Is t2 contiguous?\",t2.is_contiguous(), '\\n',\n",
    "      \"Is same data:\",t.data_ptr() == t2.data_ptr())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t3: tensor([[ 0,  4,  8],\n",
      "        [ 1,  5,  9],\n",
      "        [ 2,  6, 10],\n",
      "        [ 3,  7, 11]]) \n",
      " Is t3 contiguous? True \n",
      " Is same data: False\n"
     ]
    }
   ],
   "source": [
    "t3 = t2.contiguous()\n",
    "print('t3:',t3,'\\n',\n",
    "      \"Is t3 contiguous?\", t3.is_contiguous(),'\\n',\n",
    "      \"Is same data:\",t2.data_ptr() == t3.data_ptr())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `permute()`,`view()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[[[ 0.,  1.],\n",
      "          [ 2.,  3.]],\n",
      "\n",
      "         [[ 4.,  5.],\n",
      "          [ 6.,  7.]]],\n",
      "\n",
      "\n",
      "        [[[ 8.,  9.],\n",
      "          [10., 11.]],\n",
      "\n",
      "         [[12., 13.],\n",
      "          [14., 15.]]]])\n",
      "tensor([[ 0.,  1.,  2.,  3.,  8.,  9., 10., 11.],\n",
      "        [ 4.,  5.,  6.,  7., 12., 13., 14., 15.]])\n",
      "tensor([17.2500, 17.2500])\n"
     ]
    }
   ],
   "source": [
    "# (batch_size, channels, w, h)\n",
    "inputs = torch.arange(16, dtype=torch.float32).reshape(2,2,2,2)\n",
    "\n",
    "inputs2 = inputs.permute(1,0,2,3).contiguous().view(2,-1)\n",
    "inputs2_var = inputs2.var(1, unbiased=False)\n",
    "print(inputs)\n",
    "print(inputs2)\n",
    "print(inputs2_var)"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "### torch.stack()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[[ 1,  2,  3],\n",
      "         [ 4,  5,  6],\n",
      "         [ 7,  8,  9]],\n",
      "\n",
      "        [[10, 20, 30],\n",
      "         [40, 50, 60],\n",
      "         [70, 80, 90]]]) torch.Size([2, 3, 3])\n",
      "tensor([[[ 1,  2,  3],\n",
      "         [10, 20, 30]],\n",
      "\n",
      "        [[ 4,  5,  6],\n",
      "         [40, 50, 60]],\n",
      "\n",
      "        [[ 7,  8,  9],\n",
      "         [70, 80, 90]]]) torch.Size([3, 2, 3])\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "a = torch.tensor([[1,2,3],[4,5,6], [7,8,9]])\n",
    "b = torch.tensor([[10,20,30],[40,50,60], [70,80,90]])\n",
    "print(torch.stack([a,b], dim=0), torch.stack([a,b], dim=0).shape)\n",
    "print(torch.stack([a,b], dim=1), torch.stack([a,b], dim=1).shape)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## hook模块\n",
    "共有3个hook模块。挂在主函数上作为附加功能。\n",
    "\n",
    "`module.register_forward_hook(hook_func)`\n",
    "\n",
    "其中`hook_func(module, inputs, outputs)`是自己写的钩子函数，`inputs`是输入`module`的数据。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "a view of a leaf Variable that requires grad is being used in an in-place operation.",
     "output_type": "error",
     "traceback": [
      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
      "\u001B[0;31mRuntimeError\u001B[0m                              Traceback (most recent call last)",
      "\u001B[0;32m<ipython-input-1-4273acce651e>\u001B[0m in \u001B[0;36m<module>\u001B[0;34m\u001B[0m\n\u001B[1;32m     24\u001B[0m         \u001B[0mmodule\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mregister_forward_hook\u001B[0m\u001B[0;34m(\u001B[0m\u001B[0mforward_hook\u001B[0m\u001B[0;34m)\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0m\n\u001B[1;32m     25\u001B[0m \u001B[0;31m# 分别对两个卷积核参数进行初始化\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0m\n\u001B[0;32m---> 26\u001B[0;31m \u001B[0mnet\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mconv1\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mweight\u001B[0m\u001B[0;34m[\u001B[0m\u001B[0;36m0\u001B[0m\u001B[0;34m]\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mfill_\u001B[0m\u001B[0;34m(\u001B[0m\u001B[0;36m1\u001B[0m\u001B[0;34m)\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0m\n\u001B[0m\u001B[1;32m     27\u001B[0m \u001B[0mnet\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mconv1\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mweight\u001B[0m\u001B[0;34m[\u001B[0m\u001B[0;36m1\u001B[0m\u001B[0;34m]\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mfill_\u001B[0m\u001B[0;34m(\u001B[0m\u001B[0;36m2\u001B[0m\u001B[0;34m)\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0m\n\u001B[1;32m     28\u001B[0m \u001B[0mnet\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mconv1\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mbias\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mdata\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0mzero_\u001B[0m\u001B[0;34m(\u001B[0m\u001B[0;34m)\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0m\n",
      "\u001B[0;31mRuntimeError\u001B[0m: a view of a leaf Variable that requires grad is being used in an in-place operation."
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "class Net(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Net, self).__init__()\n",
    "        self.conv1 = nn.Conv2d(1, 2, 2, stride=(2,2), padding=0)\n",
    "        self.bn1 = nn.BatchNorm2d(2)\n",
    "    def forward(self, x):\n",
    "        x = self.conv1(x)\n",
    "        x = self.bn1(x)\n",
    "        return x\n",
    "\n",
    "def forward_hook(module, data_input, data_output):\n",
    "    print(data_input[0])\n",
    "    mean = data_input[0].mean([0, 2, 3])\n",
    "    print(mean)\n",
    "    print(module.running_mean)\n",
    "    #print(data_output)\n",
    "\n",
    "net = Net()\n",
    "# 给BN模块添加钩子函数\n",
    "for module in net.modules():\n",
    "    if isinstance(module, nn.BatchNorm2d):\n",
    "        module.register_forward_hook(forward_hook)\n",
    "# 分别对两个卷积核参数进行初始化\n",
    "net.conv1.weight[0].fill_(1)\n",
    "net.conv1.weight[1].fill_(2)\n",
    "net.conv1.bias.data.zero_()\n",
    "# 设置bn层参数\n",
    "net.bn1.weight.data.fill_(1)\n",
    "net.bn1.bias.data.fill_(5)\n",
    "fake_img = torch.ones((2,1,4,4))\n",
    "output = net(fake_img)\n",
    "#print(output.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Network Modules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 网络定义"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "\n",
    "class Net(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Net, self).__init__()\n",
    "        self.conv1 = nn.Conv2d(1, 2, 3)\n",
    "        self.bn1 = nn.BatchNorm2d(2)\n",
    "        self.relu1 = nn.ReLU()\n",
    "    def forward(self, x):\n",
    "        x = self.conv1(x)\n",
    "        x = self.bn1(x)\n",
    "        x = self.relu1(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BatchNorm模块\n",
    "batch normalization计算方法：\n",
    "1. mean:`inputs.mean([0, 2, 3])`--->维度：(channels, 1)\n",
    "2. var:将所有batch中，同一个channel的数据都按行展开，排成一行，再在每行中求var--->维度：(channels, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 0.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 初始化scale\n",
    "net.bn1.weight.data.fill_(1)\n",
    "# 初始化bias\n",
    "net.bn1.bias.data.fill_(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 网络初始化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 3)\n"
     ]
    }
   ],
   "source": [
    "net = Net()\n",
    "print(net.conv1.kernel_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `torch.optim.lr_scheduler`\n",
    "每个调整器都具有如下函数：\n",
    "* `get_last_lr`：返回一个具有上次学习率的list\n",
    "* `load_state_dict(state_dict)`：装载状态\n",
    "* `state_dict()`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型搭建"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Bad key \"text.kerning_factor\" on line 4 in\n",
      "/home/ubuntu/anaconda3/envs/pt15/lib/python3.6/site-packages/matplotlib/mpl-data/stylelib/_classic_test_patch.mplstyle.\n",
      "You probably need to get an updated matplotlibrc file from\n",
      "https://github.com/matplotlib/matplotlib/blob/v3.1.3/matplotlibrc.template\n",
      "or from the matplotlib source distribution\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim.lr_scheduler as lr_s\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class Model(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Model, self).__init__()\n",
    "        self.conv1 = nn.Conv2d(in_channels=3, out_channels=3, kernel_size=3)\n",
    "        self.relu1 = nn.ReLU()\n",
    "    def forward(self, x):\n",
    "        output = self.conv1(x)\n",
    "        output = self.relu1(x)\n",
    "        return output\n",
    "model = Model()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr = 2e-3)\n",
    "optimizer_SGD = torch.optim.SGD(model.parameters(), lr = 2e-3)\n",
    "def draw_curve(scheduler, start_epoch, epoch, str_name):\n",
    "    lr_list = []\n",
    "    for epoch in range(start_epoch, epoch+1):\n",
    "        optimizer.zero_grad()\n",
    "        optimizer.step()\n",
    "        lr_list.append(optimizer.param_groups[0]['lr'])\n",
    "        scheduler.step()\n",
    "    plt.plot(list(range(start_epoch, start_epoch+len(lr_list))), lr_list)\n",
    "    plt.xlabel('epoch')\n",
    "    plt.ylabel('lr')\n",
    "    plt.title(str_name)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `StepLR(optimizer, step_size, gamma=0.1, last_epoch=-1)`\n",
    "参数：\n",
    "* 固定epoch间隔`step_size`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stepLR = torch.optim.lr_scheduler.StepLR(optimizer, step_size=50, gamma=0.1)\n",
    "draw_curve(stepLR, 1, 200, \"stepLR\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `MultiStepLR(optimizer, milestones, gamma=0.1, last_epoch=-1)`\n",
    "参数：\n",
    "* `milestones=list()`,在指定区间里进行stepLR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stepLR = torch.optim.lr_scheduler.MultiStepLR(optimizer, [80, 120], gamma=0.1)\n",
    "draw_curve(stepLR, 1, 200, \"MultistepLR\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `CosineAnnealingLR(optimizer, T_max, eta_min=0, last_epoch=-1, verbose=False)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "epoch=100\n",
    "cos = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=epoch, eta_min=0)\n",
    "draw_curve(cos, 1, 100, \"CosineAnnelingLR\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
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     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "epoch=100\n",
    "cos = torch.optim.lr_scheduler.CosineAnnealingWarmRestarts(optimizer, T_0=5, T_mult=2)\n",
    "draw_curve(cos, 1, 500, \"CosineAnnealingWarmRestarts\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 损失函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `F.cross_enropy(outputs, targets)`\n",
    "* outputs:(batch_size, class_nums),是未经过softmax的输出\n",
    "* targets:(batch_size, 1),是标签\n",
    "\n",
    "**信息量**：用来衡量一个事件的的不确定性当一个事件发生的概率越大，不确定性越小，则他所携带的信息量就越小。我们定义\n",
    "\n",
    "**熵**：用来衡量一个系统的混乱程度，代表一个系统中的信息量的总和;信息量越大，代表这个系统的不确定性越大。\n",
    "\n",
    "假设样本空间：$\\{x_0,x_1\\}$，则事件$\\{X=x_0\\}$的信息量为：$I(x_0)=-\\log(p(x_0))$，当$p(x_0)=1$时，信息量为0。该系统的总的不确定性为所有事件的信息量的期望，也即是：\n",
    "$-p(x_0)\\log(p(x_0))-p(x_1)\\log(p(x_1))$\n",
    "\n",
    "**交叉熵**：衡量两个分布的接近程度，交叉熵越小，两分布越接近。Pytorch中的计算公式为：\n",
    "\n",
    "$H(p,q)=-\\sum_x(p(x)\\log(q(x)))$。\n",
    "\n",
    "Pytorch中的交叉熵由：softmax + log + nllloss组成"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nll_log_soft: tensor(1.1221)\n",
      "ce_loss: tensor(1.1221)\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "# 分解形式\n",
    "x_inputs = torch.randn(3,3)     #3个batch数据\n",
    "targets = torch.tensor([0,1,2])\n",
    "## 取soft_max\n",
    "soft_outputs = F.softmax(x_inputs,dim=1)\n",
    "## 取log\n",
    "log_soft = torch.log(soft_outputs)\n",
    "## 求nll损失\n",
    "nll_log_soft = F.nll_loss(log_soft, targets)\n",
    "print(\"nll_log_soft:\",nll_log_soft)\n",
    "# 组合形式\n",
    "ce_loss = F.cross_entropy(x_inputs, targets)\n",
    "print(\"ce_loss:\",ce_loss)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `F.kl_div(inputs, targets, size_average=None, reduction='mean')`\n",
    "inputs:`对数概率矩阵`，被指导者;\n",
    "\n",
    "targets：`概率矩阵`，指导者;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "kl_sum: tensor(1.5884) kl_mean: tensor(0.0794)\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn.functional as F\n",
    "torch.manual_seed(1)\n",
    "inputs = torch.randn(4,5)\n",
    "targets = torch.randn(4,5)\n",
    "inputs = F.log_softmax(inputs, dim=1)\n",
    "targets = F.softmax(targets, dim=1)\n",
    "kl_sum = F.kl_div(inputs, targets, reduction='sum')\n",
    "kl_mean = F.kl_div(inputs, targets, reduction='mean')\n",
    "print(\"kl_sum:\",kl_sum,\"kl_mean:\",kl_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 单机多卡"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `nn.DataParallel`\n",
    "使用方便，只需要用DataParallel包装模型，再设置参与训练的GPU以及汇总梯度的GPU即可。\n",
    "\n",
    "DataParallel会自动帮我们将数据切分load到相应GPU，将模型复制到相应GPU进行正向传播计算梯度并汇总。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn as nn\n",
    "from torchvision.models.resnet import resnet18\n",
    "# 模型封装\n",
    "model = resnet18()\n",
    "# model.load_state_dict(torch.load('/home/ubuntu/YZP/resnet.pt'))\n",
    "model = nn.DataParallel(model.cuda(), device_ids=[0,1,2,3], output_device=0)\n",
    "# 保存模型时要保存.module.\n",
    "torch.save(model.module.state_dict(), '/home/ubuntu/YZP/resnet2.pt')"
   ]
  }
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